Finite Group Databasebeta

← #18006068

Subgroups — #18006068

Order 4736.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558157C211yesmaximal, characteristic, complemented
2#14558148C211yesmaximal, characteristic, complemented
3#14557822C211yesmaximal, characteristic, complemented
4#14557817C211yesmaximal, characteristic, complemented
5#14557815C211yesmaximal, characteristic, complemented
6#14557792C211yesmaximal, characteristic, complemented
7#14557785C211yesmaximal, characteristic
8#14557763C211yesmaximal, characteristic, complemented
9#14557761C211yesmaximal, characteristic, complemented
10#14557756C211yesmaximal, characteristic, complemented
11#14557754C211yesmaximal, characteristic, complemented
12#14557748C211yesmaximal, characteristic, complemented
13#14557747C211yesmaximal, characteristic, complemented
14#14557558C211yesmaximal, characteristic, complemented
15C37×#476C211yesmaximal, characteristic, complemented
16C2×Dic148C2211yescharacteristic
17C2×#10596930C2211yescharacteristic
18C2×#10596940C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×#10596929C2211yescharacteristic
21C2×C8×D37C2211yescharacteristic
22#11924535C2211yescharacteristic
23#11924531—21no—
24#11924529—21no—
25#11924525—21no—
26#11924524C2211yescharacteristic
27#11924523C2211yescharacteristic
28#11924522—21no—
29#11924521—21no—
30#11924519—21no—
31#11924516C2211yescharacteristic
32#11924516C2211yescharacteristic
33#11924515—21no—
34#11924512—21no—
35#11924511C2211yescharacteristic
36#11924507C2211yescharacteristic
37C4×Dic74C2211yescharacteristic
38#11924501C2211yescharacteristic
39#11924498C2211yescharacteristic
40#11924493C2211yescharacteristic
41#11924467C2211yescharacteristic
42#11924467C2211yescharacteristic
43C4⋊#64436C2211yescharacteristic
44#11924465C2211yescharacteristic
45#11924465C2211yescharacteristic
46#11924461C2211yescharacteristic
47#11924459C2211yescharacteristic
48#11924459C2211yescharacteristic
49#11924459C2211yescharacteristic
50#11924458C2211yescharacteristic
51#11924456C2211yescharacteristic
52C4⋊Q8×C37C2211yescharacteristic
53C4×D4×C37C2211yescharacteristic
54#106×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic
57#102×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C2×Q8×C37—21no—
60C2×D4×C37C2311yescharacteristic
61C22×C4×C37—21no—
62C2×C22⋊D37—21no—
63C2×D148—21no—
64C2×D148C2311yescharacteristic
65C2×C4×D37—21no—
66C2×C4×D37C2311yescharacteristic
67C2×Dic74—21no—
68C2×Dic74C2311yescharacteristic
69C2×Dic74C2311yescharacteristic
70C2×C8×C37C2311yescharacteristic
71C2×C8×C37C2311yescharacteristic
72C4⋊C4×C37—21no—
73C4⋊C4×C37C2311yescharacteristic
74C4⋊C4×C37C2311yescharacteristic
75C4⋊C4×C37C2311yescharacteristic
76C22⋊C4×C37—21no—
77C42×C37C2311yescharacteristic
78C22⋊Dic37—21no—
79C22⋊Dic37—21no—
80C22⋊Dic37—21no—
81#10596940—41no—
82#10596939—41no—
83#10596938—21no—
84#10596938—21no—
85#10596938—21no—
86#10596938—21no—
87#10596938—21no—
88#10596938—21no—
89#10596938D411yescharacteristic
90#10596938D411yescharacteristic
91C4⋊Dic37—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37C2311yescharacteristic
94#10596936—21no—
95#10596936—21no—
96#10596936—21no—
97#10596936D411yescharacteristic
98#10596936D411yescharacteristic
99C4×Dic37—21no—
100C4×Dic37—21no—
101C4×Dic37C2311yescharacteristic
102C2×#64436C2311yescharacteristic
103C2×#64436C2311yescharacteristic
104Dic148—41no—
105#10596930—41no—
106#10596929—41no—
107C8×D37—41no—
108C23×C37—21no—
109C22×D37—21no—
110C22×D37C2×D411yescharacteristic
111Q8×C37—81no—
112D4×C37—21no—
113D4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—81no—
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2×D411yescharacteristic
120C2×C4×C37C2411yescharacteristic
121C22⋊D37—81no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37C2×D411yescharacteristic
126C2×Dic37C2×D411yescharacteristic
127C2×Dic37C2×D411yescharacteristic
128D148—21no—
129D148—21no—
130D148—81no—
131C4×D37—21no—
132C4×D37—21no—
133C4×D37—81no—
134Dic74—21no—
135Dic74—21no—
136Dic74—21no—
137Dic74—21no—
138Dic74—81no—
139C8×C37—21no—
140C8×C37—21no—
141#64436—21no—
142#64436—21no—
143C22×C37—41no—
144C22×C37—41no—
145C22×C37—41no—
146C22×C37C22×D411yescharacteristic
147C2×D37—21no—
148C2×D37—21no—
149C2×D37—21no—
150C2×D37—41no—
151C2×D37—41no—
152C2×D37—41no—
153C4×C37—21no—
154C4×C37—21no—
155C4×C37—41no—
156C4×C37—41no—
157C4×C37—41no—
158C4×C37H(5,𝔽2)11yescharacteristic
159C4×C372−1+411yescharacteristic
160Dic37—21no—
161Dic37—21no—
162Dic37—21no—
163Dic37—41no—
164Dic37—41no—
165Dic37—41no—
166#3263—371nomaximal, Sylow
167C2×C37—81no—
168C2×C37#53711yescharacteristic
169C2×C37#57711yescharacteristic
170C2×C37#57711yescharacteristic
171D37—41no—
172D37—81no—
173#542—371no—
174#542—371no—
175#476—371no—
176#476D3711yescharacteristic, complemented
177#475—371no—
178#475—371no—
179#470—371no—
180#469—371no—
181#465—371no—
182#465—371no—
183#464—371no—
184#464—371no—
185#463—371no—
186#463—371no—
187#424—371no—
188C37#326311yescharacteristic, complemented, Sylow
189C2×Q16—371no—
190C2×SD16—371no—
191C2×SD16—371no—
192C2×D8—371no—
193C2×M16—371no—
194C22×C8—371no—
195C4⋊Q8—371no—
196C4⋊Q8C2×D3711yescharacteristic
197#126—741no—
198#126—741no—
199#124—371no—
200#124—371no—
201#124—741no—
202#124—741no—
203#123—741no—
204#123—741no—
205C22⋊Q8—371no—
206C22⋊Q8—371no—
207C22⋊Q8—741no—
208C22⋊Q8—741no—
209#121—371no—
210#121—371no—
211C4×Q8—371no—
212C4×Q8—371no—
213C4×D4—371no—
214C4×D4C2×D3711yescharacteristic
215#117—371no—
216#106—371no—
217#106—371no—
218#106C2×D3711yescharacteristic
219#106C2×D3711yescharacteristic
220C4⋊C8—371no—
221C4⋊C8—371no—
222C4⋊C8—371no—
223C4⋊C8C2×D3711yescharacteristic
224#103—371no—
225#103—371no—
226#103—371no—
227#103—371no—
228#102—371no—
229#102—371no—
230#102C2×D3711yescharacteristic
231#102C2×D3711yescharacteristic
232C2×Q8—21no—
233C2×Q8—371no—
234C2×Q8—371no—
235C2×Q8—741no—
236C2×D4—371no—
237C2×D4—741no—
238C2×D4—741no—
239C2×D4C22×D3711yescharacteristic
240C22×C4—21no—
241C22×C4—371no—
242C22×C4—741no—
243Q16—1481no—
244SD16—1481no—
245SD16—1481no—
246D8—1481no—
247M16—1481no—
248C2×C8—371no—
249C2×C8—371no—
250C2×C8—1481no—
251C2×C8C22×D3711yescharacteristic
252C2×C8C22×D3711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—371no—
255C4⋊C4—371no—
256C4⋊C4—371no—
257C4⋊C4—741no—
258C4⋊C4—741no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4—741no—
262C4⋊C4C22×D3711yescharacteristic
263C4⋊C4C22×D3711yescharacteristic
264C4⋊C4C22×D3711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—371no—
267C22⋊C4—371no—
268C22⋊C4—741no—
269C22⋊C4—741no—
270C22⋊C4—741no—
271C22⋊C4—741no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4—741no—
276C22⋊C4—741no—
277C42—371no—
278C42—741no—
279C42—741no—
280C42C22×D3711yescharacteristic
281C23—21no—
282C23—371no—
283C23—741no—
284Q8—81no—
285Q8—2961no—
286Q8—741no—
287Q8—741no—
288Q8—741no—
289Q8—741no—
290D4—21no—
291D4—21no—
292D4—2961no—
293D4—2961no—
294D4—741no—
295D4—741no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—371no—
301C2×C4—371no—
302C2×C4—371no—
303C2×C4—2961no—
304C2×C4—741no—
305C2×C4—741no—
306C2×C4—741no—
307C2×C4—741no—
308C2×C4—741no—
309C2×C4D4×D3711yescharacteristic
310C2×C4D4×D3711yescharacteristic
311C2×C4C23×D3711yescharacteristic
312C8—21no—
313C8—21no—
314C8—741no—
315C8—741no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—741no—
320C22—741no—
321C22—741no—
322C22—1481no—
323C22—1481no—
324C22—1481no—
325C22C2×D4×D3711yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—741no—
332C4—741no—
333C4—741no—
334C4—1481no—
335C4—1481no—
336C4—1481no—
337C4#1192458211yescharacteristic
338C4#1192458411yescharacteristic
339C2—81no—
340C2—2961no—
341C2—1481no—
342C2#1455811311yescharacteristic
343C2#1455833911yescharacteristic
344C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#476C2
socleC22×C37C22×D4
prime radical#14557785C2
hypercenter#476D37
hypocenterC37#3263
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14558157C2semidirect
2. #14558148C2semidirect
3. #14557822C2semidirect
4. #14557817C2semidirect
5. #14557815C2semidirect
6. #14557792C2semidirect
8. #14557763C2semidirect
9. #14557761C2semidirect
10. #14557756C2semidirect
11. #14557754C2semidirect
12. #14557748C2semidirect
13. #14557747C2semidirect
14. #14557558C2semidirect
15. C37×#476C2semidirect
176. #476D37semidirect
188. C37#3263semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145581572
#145581482
#145578222
#145578172
#145578152
#145577922
#145577852
#145577632
#145577612
#145577562
#145577542
#145577482
#145577472
#145575582
C37×#4762
#326337